Scanner characterization traditionally suffers from a compromise between very data intensive fitting or simplified model based characterization with less accuracy than is desired for using the scanner for subsequent printer calibration. The emphasis on scanner calibration in the past was calibration for unknown inputs—either unknown grey component replacement strategy or unknown input media. This meant that the calibration was an attempt to do well in a larger domain of inputs, rather than doing very well in a restricted domain.
To characterize a scanner for printer calibration, typically a number of patches of various colors are printed, measured with a known instrument (such as a spectrophotometer), scanned and patch averages are computed.
The usual goal of scanner characterization is to obtain the best possible result when scanning pages of unknown origin. Such pages may or may not be halftones, and they typically contain image content, rather than simple collections of constant patches. Lack of information regarding paper color (and fluorescence) and colorant materials limits the quality of such characterizations.
Sharma et al., G. Sharma, S. Wang, D. Sidavanahalli and K. Knox “The impact of UCR on scanner calibration”, in Proc PICS Conf., pp. 121-124, Portland, Oreg. (1998) describe the impact an unknown amount of black substitution can have on scanner characterization. In the worst case, they found errors as high as 4.5 (mean ΔE), while when it was fully known, mean errors dropped below 1.2. When calibrating printers, there is generally no black substitution. It suffices to characterize the scanner for this case.
Many others have characterized scanners. Ostromoukhov et al., V. Ostromoukhov, R. D. Hersch, C. Péraire, P. Emmel, I. Amidror, “Two approaches in scanner-printer calibration: calorimetric space-based vs. closed-loop”, in Proc SPIE 2170, pp. 133-142(1994) obtained results of 2.37 (mean ΔE). One reason for their poorer results is that the printer was a desktop inkjet printer, with more noise and lower stability than the Xerographic printer used by Sharma et al. They noted neighborhood effects, and attempted to reduce their impact by using large patches. This may give incorrect results. Hardeberg, J. Hardeberg, “Desktop Scanning to sRGB” in IS&T and SPIE's Device Independent Color, Color Hardcopy and Graphic Arts V, San Jose, Calif. (January 2000), optimized a third order (3×20) matrix, obtaining ΔE 1.4 on two scanners, with less good results on others. Previously, Haneishi et al., H. Haneishi, T. Hirao, A. Shimazu, and Y. Miyake, “Colorimetric precision in scanner calibration using matrices”, in Proceedings of IS&T and SID'S 3rd Color Imaging Conference: Color Science, Systems and Applications, pp. 106-108, Scottsdale, Ariz. (November 1995), had obtained ΔE=2 using a second (3×10) matrix regression. Rao, A. R. Rao, “Color calibration of a colorimetric scanner using non-linear least squares”, in Proc. IS&T's 1998 PICS Conference, Portland, Oreg. (May 1998), obtained similar values. Hardeberg's thesis, J. Hardeberg, Acquisition and Reproduction of Colour Images: Colorimetric and Multispectral Approaches, Doctoral Dissertation, l'Ecole Nationale Supérieure des Télécommunications (Paris 1999), describes an experiment (p. 37ff.) in which a single scanner is characterized with a mean ΔE of 0.92, a max of 4.67 and a 95th percentile of 2.25 on a set of 288 patches (the same set used to calibrate). He also characterized and tested on (disjoint) subsets (p. 51), and found that when he used 144 patches to train, and the other 144 to test, the mean ΔE rose to 0.96, but the max (of the test set) fell to 3.36 (the max ΔE for the training set was higher, at 3.9).
Because scanners are not colorimetric, they may exhibit metamerism: colors that appear identical to a scanner might appear different to a human observer. For fixed media and black substitution strategy metamerism is not a problem. However, the conversion from RGB to XYZ various throughout color space. As compensation, scanners may measure far more patches per minute than spectrophotometers inasmuch as we can afford to sample color space substantially more densely.
The only difference between characterizing a scanner for printer calibration and characterizing it for arbitrary prints from that printer is the sampling of color space. While there is no need to characterize the scanner in regions of color space which are not used for printer calibration, all regions are typically sampled in the more general case.
By way of background, methods of printer calibration are described, with particular reference to the portions of color space they each seek to control.
One type of printer calibration involves ΔE from paper. For this printer calibration, a step wedge in each separation is used. In better implementations, the step wedge is linear in ΔE distance from paper, as predicted by the previous calibration. As a result, we cannot predict exactly which color will be needed but we can say they will be along the CMYK axes. These axes do not (exactly) run along lines in L*a*b* space, but they are confined to space curves, which stay relatively fixed. That is, it is sufficient to be able to estimate the location along the curve, and ignore any deviation from the curve. What matters is the ability of the measuring device (in this case a scanner) to detect small changes along that line.
Another type of printer calibration uses Grey Balance Tone Reproduction Curves (TRC). For this calibration, patches surrounding the presumed neutral axis are printed and measured, in order to find a better approximation of the location of the neutral axis. The neutral axis is then divided into equal increments along L* and CMY points along that axis define the TRCs. The neutral axis does not generally go to the full CMY point, as one of the three defines the limit of the CMY neutral. The others are then smoothly carried out to their limits. The procedure normally begins with a good estimate of the printer response, from a combination of a full characterization and any previous grey balance calibrations. The refinement is only CMY patches close to the neutral axis. A separate ΔE from paper TRC is built for the black separation.
In terms of being able to do a grey balance TRC with a scanner, the issue is how well can the scanner be calibrated near the neutral axis, and, once calibrated, how sensitive is it to small changes in both lightness along the axis and changes perpendicular to the axis.
Another type of printer calibration uses a two-dimensional tone reproduction curve (TRC). In this version, there are three two dimensional tables built, for CMY space. One maps from (C, M+Y) to C′, another from (M, C+Y) to M′, and the third from (Y, C+M) to Y′. Considering only the first one, the table is built with ΔE from paper along the M+Y=0 axis, grey balance along the line C=(M+Y)/2, ΔE from red along the line from white to red, ΔE from red along the line from red to black, and ΔE from cyan along the line from cyan to black. One other line is typically controlled, using a compromise between ΔE from paper to blue and to green along the line from (0,0) to (0,1). Similar lines are controlled for the other two tables. This means that the following lines through color space are controlled: paper to C, M, Y, R, G, B; paper to CMY; CMY to C, M, Y, R, G and B; paper to K. Many of these are lines that were controlled in one of the prior two calibrations. The new lines are all controlled in a one-dimensional sense, just as for the ΔE from paper calibration, so again, the only thing that substantially matters for them is the scanner response to small changes along a curve, and not orthogonal to the curve.
Still another type of printer calibration involves a three-dimensional tone reproduction curve (TRC). In this version, all of color space is sampled, but coarsely. That is, a relatively coarse grid in CMY space is used to obtain a 3D correction function. If, e.g. a 7×7×7 grid of CMY points is used to calibrate the printer, it is colors in the neighborhood of those 343 patches that matter.